Definition:Contingent Statement
Contents |
Definition
A contingent statement is a statement form which is neither a tautology nor a contradiction, but whose truth value depends upon the truth value of its component substatements.
Logical Formula
In the context of logical formulas the term satisfiable is usually used:
A logical formula $P$ is satisfiable if its value is True in at least one boolean interpretation.
A logical formula $P$ is not-valid or falsifiable if its value is False in at least one boolean interpretation.
Set of Logical Formulas
Let $U = \left\{{P_1, P_2, \ldots, P_n}\right\}$ be a set of logical formulas.
Let $U' = \left\{{p_1, p_2, \ldots, p_m}\right\}$ be the set of all the atoms of all the logical formulas in $U$.
(Some of these atoms, and indeed this will most likely be the case, may be in more than one logical formula.)
Then $U$ is (mutually) satisfiable if there exists a boolean interpretation $v$ for all the atoms in $U'$ such that $v \left({P_1}\right) = v \left({P_2}\right) = \cdots = v \left({P_n}\right) = T$.
Also see
Sources
- D.J. O'Connor and Betty Powell: Elementary Logic (1980): $\S 1.3$
